#### Answer

$\dfrac{1}{2}r^{2}t^{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[4]{\dfrac{1}{16}r^{8}t^{20}}
,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers.
$\bf{\text{Solution Details:}}$
Expressing the radicand of the expression above with a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[4]{\left(\dfrac{1}{2}r^{2}t^{5}\right)^4}
\\\\=
\dfrac{1}{2}r^{2}t^{5}
.\end{array}